Dislocation Interactions in Olivine Control Postseismic Creep of the Upper Mantle

Dislocation interactions in olivine control postseismic creep of the upper mantle David Wallis1†*, Lars N. Hansen2, Angus J. Wilkinson3, Ricardo A. Lebensohn4 1Department of Earth Sciences, Utrecht University, 3584 CB Utrecht, The Netherlands. 2Department of Earth Science, University of Minnesota-Twin Cities, Minneapolis, Minnesota, U.S.A. 55455. 3Department of Materials, University of Oxford, Oxford, OX1 3PH, U.K. 4Los Alamos National Laboratory, Los Alamos, New Mexico, U.S.A. †Present address: Department of Earth Sciences, University of Cambridge, Cambridge, CB2 3EQ, U.K. *Corresponding author Abstract Changes in stress applied to mantle rocks, such as those imposed by earthquakes, induce a period of evolution in viscosity and microstructure. This transient creep is often modelled based on stress transfer among slip systems due to grain interactions. However, recent experiments have demonstrated that the intragranular accumulation of stresses among dislocations is the dominant cause of strain hardening in olivine at low temperatures, raising the question of whether the same process contributes to transient creep at higher temperatures. Here, we demonstrate that olivine samples deformed at 25°C or 1150–1250°C both contain stress heterogeneities of ~1 GPa that are imparted by dislocations and have correlation lengths of ~1 μm. The similar stress distributions formed in both temperature regimes indicate that accumulation of stresses among dislocations also provides a contribution to transient creep at high temperatures. The results motivate a new generation of models that capture these intragranular processes and may refine predictions of evolving mantle viscosity over the earthquake cycle. Introduction Major earthquakes impose changes in stress on the hotter, viscous rocks underlying the fault zone1–7. Relaxation of these stresses contributes to postseismic deformation and stress redistribution within and between fault zones over the earthquake cycle1–7. Modelling these processes is challenging because changes in the stress applied to viscous rocks induce a period of transient evolution in viscosity, which is observable in laboratory experiments8–14 and detectable in geodetic datasets1–4,15. In both these contexts, the observations are often best fit by rheological models with nonlinear stress dependencies indicating that dislocation motion plays a dominant role1–4,8–10. Experiments on geological minerals9,16–18 and metals19,20 have demonstrated that this transient creep results from subtle changes in the dislocation microstructure and/or micromechanical state in response to a change in applied stress. Constraints on these underlying microphysical processes are therefore key to the formulation of rheological models that can be confidently extrapolated between laboratory and natural deformation conditions. 1 Previous studies have considered rheological behaviours typical of both low-temperature and high- temperature conditions to contribute to postseismic transient creep. Geological studies have focused on deformation microstructures in exhumed shear zones that are inferred to have directly underlain frictional faults, in which the stress changes and their associated microstructural expressions are most pronounced6,21. In these settings, postseismic deformation is recorded by dislocation microstructures (e.g., slip bands and cells of tangled dislocations) associated with low-temperature plasticity that is inferred to have been induced by transient increases in stress6,21. In contrast, postseismic geodetic signals can capture far-field deformation distributed throughout the lower crust and upper mantle, for which temperatures are typically higher and stress changes are smaller than directly adjacent to the seismogenic zone1–4,15,22. In these contexts, deformation by dislocation creep or dislocation-accommodated grain boundary sliding is likely commonplace23–25. Most quantitative descriptions of transient creep used to analyse postseismic geodetic data are largely phenomenological in that they describe observed material behaviour but lack a comprehensive basis in the underlying physical processes. A widely used example is the Burgers rheology1,2,26–28, which is capable of generating a time-dependent evolution in viscosity, anelastic behaviour, and steady-state flow. Whilst attempts have been made to link a Burgers rheology to transient dislocation creep1,2,28, the overarching arrangement of the Maxwell and Kelvin elements does not arise naturally from the fundamentals of dislocation motion. A model with a deeper basis in the microphysics of dislocation creep has been proposed by Karato29, inspired by earlier experiments on water ice12,13. In this model, transient creep arises from stress transfer between populations of grains with different crystallographic orientations. Upon loading, initial dislocation motion occurs in grains with high resolved shear stress on the weakest slip system. However, maintenance of strain compatibility in an aggregate of anisotropic grains requires activation of additional, stronger slip systems in other grains to counteract stress concentrations generated during progressive deformation. This progressive transition in the slip systems that control the bulk strain rate results in a progressive increase in viscosity29. Whilst the transfer of stress among slip systems in grains of different orientations does potentially contribute to transient creep of rocks, a variety of studies have demonstrated that transient creep also occurs even in single crystals, for which the stress-transfer model cannot apply. Strain hardening transients are exhibited by single crystals of olivine deforming by both low-temperature plasticity30–32 and power-law creep at high temperatures9,33,34, with the transition between mechanisms occurring at temperatures of approximately 1000–1100°C at typical experimental stresses and strain rates. Microstructural analyses of single crystals deformed in both temperature regimes indicate that strain hardening results from increases in dislocation density9,35,36 and long-range interactions among dislocations via their stress fields36,37. These observations imply that these intragranular processes make an essential contribution to strain-hardening transients that has been largely overlooked. This suggestion is supported by a comparison between strain hardening behaviour of single crystals and that of aggregates of olivine deformed at room temperature, which are indistinguishable31. Therefore, it seems clear that transient creep of aggregates deformed in low-temperature plasticity is controlled by intragranular dislocation interactions. However, a major outstanding question remains. Do similar interactions among dislocations contribute to transient deformation at the high temperatures relevant to the regions of the lithosphere contributing to postseismic creep? 2 We hypothesise that the same intragranular processes control transient creep of aggregates of olivine deformed by power-law creep and those deformed by low-temperature plasticity. We suggest that samples deformed in either regime will share similarities in characteristics of their residual stress fields. Specifically, we test for the presence of intragranular stress heterogeneity, whether that heterogeneity can be attributed to the dislocation content, and whether that heterogeneity occurs over length-scales greater than the average dislocation spacing, indicating the stresses arise from long-range dislocation interaction. We carry out these tests by analysing intragranular stress heterogeneity within olivine deformed at either 25°C31 or 1150–1250°C23 using high-angular resolution electron backscatter diffraction (HR-EBSD) (Methods). Unlike conventional EBSD, which struggles to resolve the subtle microstructural changes associated with transient creep at small strains38, HR-EBSD provides exceptionally precise estimates of the density of geometrically necessary dislocations and, importantly, maps heterogeneity in elastic strain and residual stress39–42. We analyse the stress distributions in terms of the theory, established in the materials sciences43–45, for stress fields of a population of dislocations to test the causality between stress heterogeneity and the dislocation content (Methods). In particular, we test whether tails of the probability -3 (P) distributions of shear stress (σ12) follow a P(σ12) ∝ σ12 relationship, as expected of stress fields generated by dislocations43–46 (Methods). Autocorrelation of the stress fields provides a measure of the characteristic length scale of stress variation (Methods) and therefore a test for the presence of long-range internal stress. If the hypothesis is supported by our results, these observations will provide the basis for a new generation of rheological models of transient creep, rooted in the microphysics of intracrystalline deformation. Results Geometrically necessary dislocation density Figure 1 presents maps of the densities of geometrically necessary dislocations in each sample. The undeformed single crystal, MN1, exhibits an apparent density of approximately 1×1012 m-2, resulting from noise in the rotation measurements47. This value is consistent with a total dislocation density of < 1010 m-2 measured previously by oxidation decoration47. The undeformed aggregate, PI-1523s, contains GND densities generally < 1014 m-2, but with some grains dissected by bands of GND densities > 1014 m-2 that mark subgrain boundaries. The single crystal deformed at room temperature, San382t,

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